Question

If \( \tan \theta = \sqrt{n} \) for some non-square natural number \( n \), then sec \( 2\theta \) is:

• A. A rational number
• B. An irrational number
• C. A positive number
• D. None of the above

Hint:

When the tangent of an angle is a square root of a non-square number, the secant value typically results in an irrational number.

Answer 1

The Correct Option is B

For \( \tan \theta = \sqrt{n} \), secant of \( 2\theta \) can be derived using trigonometric identities. The result will be an irrational number.
Final Answer: \[ \boxed{\text{An irrational number}} \]